On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces
Annales de l'Institut Fourier, Volume 43 (1993) no. 3, pp. 655-712.

The continuous cohomology theory of the Lie algebra L(M) of complex analytic vector fields on an open Riemann surface M is studied. We show that the cohomology group with coefficients in the L(M)-module of germs of complex analytic tensor fields on the product space M n decomposes into the global part derived from the homology of M and the local part coming from the coefficients.

Dans cet article nous étudions la cohomologie continue de l’algèbre de Lie L(M) des champs de vecteurs analytiques complexes sur une surface de Riemann ouverte M. Nous montrons que le groupe de cohomologie à coefficients dans le L(M)-module des germes de champs de tenseurs analytiques complexes sur le produit M n se décompose en la partie globale dérivée de l’homologie de M et la partie locale provenant des coefficients.

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     author = {Kawazumi, Nariya},
     title = {On the complex analytic {Gel'fand-Fuks} cohomology of open {Riemann} surfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {655--712},
     publisher = {Imprimerie Louis-Jean},
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     volume = {43},
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     year = {1993},
     doi = {10.5802/aif.1351},
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     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1351/}
}
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Kawazumi, Nariya. On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces. Annales de l'Institut Fourier, Volume 43 (1993) no. 3, pp. 655-712. doi : 10.5802/aif.1351. https://aif.centre-mersenne.org/articles/10.5802/aif.1351/

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